The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical propertie...The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.展开更多
Considering arch rib, lateral brace, suspender, girder, pier and track position, the model for the interaction between long-span tied arch continuous bridge and multiple tracks was established by using steel-concrete ...Considering arch rib, lateral brace, suspender, girder, pier and track position, the model for the interaction between long-span tied arch continuous bridge and multiple tracks was established by using steel-concrete composite section beam element to simulate concrete-filled steel tube(CFST) arch rib, using the beam element with rigid arm to simulate the prestressed concrete girder and using nonlinear bar element to simulate longitudinal constraint between track and bridge. Taking a(77+3×156.8+77) m tied arch continuous bridge with four tracks on the Harbin-Qiqihar Passenger Dedicated Line as an example, the arrangement of continuously welded rail(CWR) was explored. The longitudinal force in CWR on the tied arch continuous bridge, the pier top horizontal force and torque due to the unbalance load case, were analyzed under the action of temperature, vertical live load, train braking and wind load.Studies show that, it can significantly reduce track displacement to set the track expansion devices at main span arch springing on both sides; the track stress due to arch temperature variation can reach 40.8 MPa; the track stress, pier top horizontal force and torque are related to the number of loaded tracks and train running direction, and the bending force applied to unloaded track is close to the loaded track, while the braking force applied to unloaded track is 1/4 to 1/2 of the loaded track; the longitudinal force of track due to the wind load is up to 12.4 MPa, which should be considered.展开更多
A new mechanics model, which reveals additional longitudinal force transmission between the continuously welded rails and the bridges, is established on the fact that the influence of the mutual relative displacement ...A new mechanics model, which reveals additional longitudinal force transmission between the continuously welded rails and the bridges, is established on the fact that the influence of the mutual relative displacement (among) the rail, the sleeper and the beam is taken into account. An example is presented and numerical results are compared. The results show that the additional longitudinal forces calculated with the new model are less than those of the previous, especially in the case of the flexible pier bridges. The new model is also suitable for the analysis of the additional longitudinal force transmission between rails and bridges of ballastless track with small resistance fasteners without taking the sleeper displacement into account, and compared with the ballast bridges, the ballastless bridges have a much stronger additional longitudinal force transmission between the continuously welded rails and the bridges.展开更多
This paper describes the economic and technological benefits of installing continuous welded rail (CWR) track on sharp (radius≤300 m) railway curves. A new form of prestressed concrete sleepers developed by the V...This paper describes the economic and technological benefits of installing continuous welded rail (CWR) track on sharp (radius≤300 m) railway curves. A new form of prestressed concrete sleepers developed by the V. Lazaryan Dniprope- trovsk National University of Railway Transport is shown to improve the lateral shift resistance of CWR track in sharp curves and the use of anchor sleepers on tangents is shown to make it possible to lower the fastening temperature of the CWR track in order to increase the rail lifespan.展开更多
Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint ...Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.展开更多
X-style arch bridge on high-speed railways(HSR)is one kind of complicated long-span structure,and the track-bridge interaction is essential to ensure the safety and smoothness of HSR.Taking an X-style steel-box arch b...X-style arch bridge on high-speed railways(HSR)is one kind of complicated long-span structure,and the track-bridge interaction is essential to ensure the safety and smoothness of HSR.Taking an X-style steel-box arch bridge with a main span of450 m on HSR under construction for example,a new integrative mechanic model of rail-stringer-cross beam-suspenderpier-foundation coupling system was established,adopting the nonlinear spring element simulating the longitudinal resistance between track and bridge.The transmission law of continuous welded rail(CWR)on the X-style arch bridge was researched,and comparative study was carried out to discuss the influence of several sensitive factors,such as the temperature load case,the longitudinal resistance model,the scheme of longitudinal restraint conditions,the introverted inclination of arch rib,the stiffness of pier and abutment and the location of the rail expansion device.Calculating results indicate that the longitudinal resistance has a significant impact upon the longitudinal forces of CWR on this kind of bridge,while the arch rib’s inclination has little effect.Besides,temperature variation of arch ribs and suspenders should be taken into account in the calculation.Selecting the restraint system without longitudinally-fixed bearing and setting the rail expansion devices on both ends are more reasonable.展开更多
The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation an...The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.展开更多
By building the finite element model, the track parameters, including the ultimate longitudinal resistance, the length of the intermediate straight line, and the gap between spacer blocks, were analyzed for their infl...By building the finite element model, the track parameters, including the ultimate longitudinal resistance, the length of the intermediate straight line, and the gap between spacer blocks, were analyzed for their influences on the longitudinal forces and displacements of the single turnout and turnout group, respectively. The results indicate that when the longitudinal resistance drops from 32 to 20 N/cm, the maximum additional longitudinal force of the turnout group increases by 19. 2%, and the maximum additional longitudinal displacement of the turnout group grows by 85.3% compared with 50.4% for the single turnout. When the length of intermediate straight line rises from 0 m to infinite, the maximum additional longitudinal force decreases by 38.8%, and the maximum additional longitudinal displacement by 80.3%.展开更多
As a vehicle passing through a track with different weld irregularities, the dynamic performance of track com- ponents is investigated in detail by using a coupled vehi- cle-track model. In the model, the vehicle is m...As a vehicle passing through a track with different weld irregularities, the dynamic performance of track com- ponents is investigated in detail by using a coupled vehi- cle-track model. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom, and a Timoshenko beam is used to model the rails which are dis- cretely supported by sleepers. In the track model, the sleepers are modeled as rigid bodies accounting for their vertical, lat- eral and rolling motions and assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the study of the coupled vehicle and track dynamics, the Hertizian contact theory and the theory proposed by Shen-Hedrick-Elkins are, respectively, used to calculate normal and creep forces between the wheel and the rails. In the calculation of the normal forces, the coefficient of the normal contact stiffness is determined by transient contact condition of the wheel and rail surface. In the calcu- lation of the creepages, the lateral, roll-over motions of the rail and the fact that the relative velocity between the wheel and rail in their common normal direction is equal to zero are simultaneously taken into account. The motion equations of the vehicle and track are solved by means of an explicit integration method, in which the rail weld irregularities are modeled as local track vertical deviations described by some ideal cosine functions. The effects of the train speed, the axle load, the wavelength and depth of the irregularities, and the weld center position in a sleeper span on the wheel-rail impact loading are analyzed. The numerical results obtained are greatly useful in the tolerance design of welded rail pro- file irregularity caused by hand-grinding after rail welding and track maintenances.展开更多
An innovation is conducted on a K190πK rail auto welding machine because of its poor stability in quality of welding joints. A new control system based on a programmable controller is designed to replace the old o...An innovation is conducted on a K190πK rail auto welding machine because of its poor stability in quality of welding joints. A new control system based on a programmable controller is designed to replace the old one. The new control system is of higher accuracy in controlling sequence and good ability in anti disturbance, and is convenient to operate. The comparison tests are carried out. The experimental results show that the quality of welded joints is greatly increased by the improved welding mechine.展开更多
To get the influence of the randomness of longitudinal resistance of ballast bed (LRBB) on track-bridge interaction, the statistical law of LRBB was studied with existing test data and the Shapiro-Wilk test. Based on ...To get the influence of the randomness of longitudinal resistance of ballast bed (LRBB) on track-bridge interaction, the statistical law of LRBB was studied with existing test data and the Shapiro-Wilk test. Based on the principle of track-bridge interaction, a rail-sleeper-bridge-pier integrated simulation model that could consider the randomness of LRBB was established. Taking a continuous beam bridge for the heavy-haul railway as an example, the effect of the randomness of LRBB on the mechanical behavior of continuous welded rail (CWR) on bridges under typical conditions was carefully examined with a random sampling method and the simulation model. The results show that the LRBB corresponding sleeper displacement of 2 mm obeys a normal distribution. When the randomness of LRBB is considered, the amplitudes of rail expansion force, rail bending force, rail braking force and rail broken gap all follow normal distribution. As the standard deviations of the four indexes are small, which indicates the randomness of LRBB has little effect on track-bridge interaction. The distributions of the four indexes make it possible to design CWR on bridges with the limit state method.展开更多
Manuscript received 30 July 1999 Abstract The shielded metal arc welding (SMAW) of a manganese steel part as a crossing of railway track to a carbon steel part as the rails of the railroad is the welding of dissimil...Manuscript received 30 July 1999 Abstract The shielded metal arc welding (SMAW) of a manganese steel part as a crossing of railway track to a carbon steel part as the rails of the railroad is the welding of dissimilar steel. It are was known that it is not possible to the the rail of railroad directly to the cross- ing of railway track made from a steel containing about 14% of manganese (wt. ) because of so many differences between the two kinds of steels such as composition, microstructure,mechanical properties and weldability.A method was used to solve the problem by presetting an intermediate layer on each side of the joint and other special procedures were used.The result of test indicated that a good weld joint was obtained.展开更多
It is known from our former theoretical analysis that the single-inclined welding surface which is inclined towards the transverse direction of the rail can only eliminate vertical bumping, and the single-inclined wel...It is known from our former theoretical analysis that the single-inclined welding surface which is inclined towards the transverse direction of the rail can only eliminate vertical bumping, and the single-inclined welding surface which is inclined towards the vertical direction of the rail can only eliminate lateral vibration. In this paper, we put forward a welding structure of double-inclined welding surface to eliminate the vertical bumping and lateral vibration at the same time, and analyze the stress state of continuous welded rail (CWR) by combining geometrical azimuth. Furthermore, the increase of bearing capacity of CWR with the double-inclined welding surface is theoretically analyzed.展开更多
基金supported by the National Key R&D Program of China(2022YFB2602901)the National Natural Science Foundation of China(No.52178405).
文摘The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.
基金Project(51378503)supported by the National Natural Science Foundation of ChinaProject(2014M552158)supported by China Postdoctoral Science Foundation
文摘Considering arch rib, lateral brace, suspender, girder, pier and track position, the model for the interaction between long-span tied arch continuous bridge and multiple tracks was established by using steel-concrete composite section beam element to simulate concrete-filled steel tube(CFST) arch rib, using the beam element with rigid arm to simulate the prestressed concrete girder and using nonlinear bar element to simulate longitudinal constraint between track and bridge. Taking a(77+3×156.8+77) m tied arch continuous bridge with four tracks on the Harbin-Qiqihar Passenger Dedicated Line as an example, the arrangement of continuously welded rail(CWR) was explored. The longitudinal force in CWR on the tied arch continuous bridge, the pier top horizontal force and torque due to the unbalance load case, were analyzed under the action of temperature, vertical live load, train braking and wind load.Studies show that, it can significantly reduce track displacement to set the track expansion devices at main span arch springing on both sides; the track stress due to arch temperature variation can reach 40.8 MPa; the track stress, pier top horizontal force and torque are related to the number of loaded tracks and train running direction, and the bending force applied to unloaded track is close to the loaded track, while the braking force applied to unloaded track is 1/4 to 1/2 of the loaded track; the longitudinal force of track due to the wind load is up to 12.4 MPa, which should be considered.
文摘A new mechanics model, which reveals additional longitudinal force transmission between the continuously welded rails and the bridges, is established on the fact that the influence of the mutual relative displacement (among) the rail, the sleeper and the beam is taken into account. An example is presented and numerical results are compared. The results show that the additional longitudinal forces calculated with the new model are less than those of the previous, especially in the case of the flexible pier bridges. The new model is also suitable for the analysis of the additional longitudinal force transmission between rails and bridges of ballastless track with small resistance fasteners without taking the sleeper displacement into account, and compared with the ballast bridges, the ballastless bridges have a much stronger additional longitudinal force transmission between the continuously welded rails and the bridges.
文摘This paper describes the economic and technological benefits of installing continuous welded rail (CWR) track on sharp (radius≤300 m) railway curves. A new form of prestressed concrete sleepers developed by the V. Lazaryan Dniprope- trovsk National University of Railway Transport is shown to improve the lateral shift resistance of CWR track in sharp curves and the use of anchor sleepers on tangents is shown to make it possible to lower the fastening temperature of the CWR track in order to increase the rail lifespan.
文摘Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.
基金Projects(51378503,51178471) supported by the National Natural Science Foundation of China
文摘X-style arch bridge on high-speed railways(HSR)is one kind of complicated long-span structure,and the track-bridge interaction is essential to ensure the safety and smoothness of HSR.Taking an X-style steel-box arch bridge with a main span of450 m on HSR under construction for example,a new integrative mechanic model of rail-stringer-cross beam-suspenderpier-foundation coupling system was established,adopting the nonlinear spring element simulating the longitudinal resistance between track and bridge.The transmission law of continuous welded rail(CWR)on the X-style arch bridge was researched,and comparative study was carried out to discuss the influence of several sensitive factors,such as the temperature load case,the longitudinal resistance model,the scheme of longitudinal restraint conditions,the introverted inclination of arch rib,the stiffness of pier and abutment and the location of the rail expansion device.Calculating results indicate that the longitudinal resistance has a significant impact upon the longitudinal forces of CWR on this kind of bridge,while the arch rib’s inclination has little effect.Besides,temperature variation of arch ribs and suspenders should be taken into account in the calculation.Selecting the restraint system without longitudinally-fixed bearing and setting the rail expansion devices on both ends are more reasonable.
基金Project(2021RC2011)supported by the Science and Technology Innovation Program of Hunan Province,ChinaProjects(U1934207,52178180)supported by the National Natural Science Foundation of ChinaProject(2021M703648)supported by the China Postdoctoral Science Foundation。
文摘The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.
基金The Doctoral Fund of Ministry of Educa-tionof China (No. 20050613007)
文摘By building the finite element model, the track parameters, including the ultimate longitudinal resistance, the length of the intermediate straight line, and the gap between spacer blocks, were analyzed for their influences on the longitudinal forces and displacements of the single turnout and turnout group, respectively. The results indicate that when the longitudinal resistance drops from 32 to 20 N/cm, the maximum additional longitudinal force of the turnout group increases by 19. 2%, and the maximum additional longitudinal displacement of the turnout group grows by 85.3% compared with 50.4% for the single turnout. When the length of intermediate straight line rises from 0 m to infinite, the maximum additional longitudinal force decreases by 38.8%, and the maximum additional longitudinal displacement by 80.3%.
基金supported by the National Basic Research Program of China(2007CB714702)the National Natural Science Foundation of China(50821063,50675183 and 50875221)
文摘As a vehicle passing through a track with different weld irregularities, the dynamic performance of track com- ponents is investigated in detail by using a coupled vehi- cle-track model. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom, and a Timoshenko beam is used to model the rails which are dis- cretely supported by sleepers. In the track model, the sleepers are modeled as rigid bodies accounting for their vertical, lat- eral and rolling motions and assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the study of the coupled vehicle and track dynamics, the Hertizian contact theory and the theory proposed by Shen-Hedrick-Elkins are, respectively, used to calculate normal and creep forces between the wheel and the rails. In the calculation of the normal forces, the coefficient of the normal contact stiffness is determined by transient contact condition of the wheel and rail surface. In the calcu- lation of the creepages, the lateral, roll-over motions of the rail and the fact that the relative velocity between the wheel and rail in their common normal direction is equal to zero are simultaneously taken into account. The motion equations of the vehicle and track are solved by means of an explicit integration method, in which the rail weld irregularities are modeled as local track vertical deviations described by some ideal cosine functions. The effects of the train speed, the axle load, the wavelength and depth of the irregularities, and the weld center position in a sleeper span on the wheel-rail impact loading are analyzed. The numerical results obtained are greatly useful in the tolerance design of welded rail pro- file irregularity caused by hand-grinding after rail welding and track maintenances.
文摘An innovation is conducted on a K190πK rail auto welding machine because of its poor stability in quality of welding joints. A new control system based on a programmable controller is designed to replace the old one. The new control system is of higher accuracy in controlling sequence and good ability in anti disturbance, and is convenient to operate. The comparison tests are carried out. The experimental results show that the quality of welded joints is greatly increased by the improved welding mechine.
文摘To get the influence of the randomness of longitudinal resistance of ballast bed (LRBB) on track-bridge interaction, the statistical law of LRBB was studied with existing test data and the Shapiro-Wilk test. Based on the principle of track-bridge interaction, a rail-sleeper-bridge-pier integrated simulation model that could consider the randomness of LRBB was established. Taking a continuous beam bridge for the heavy-haul railway as an example, the effect of the randomness of LRBB on the mechanical behavior of continuous welded rail (CWR) on bridges under typical conditions was carefully examined with a random sampling method and the simulation model. The results show that the LRBB corresponding sleeper displacement of 2 mm obeys a normal distribution. When the randomness of LRBB is considered, the amplitudes of rail expansion force, rail bending force, rail braking force and rail broken gap all follow normal distribution. As the standard deviations of the four indexes are small, which indicates the randomness of LRBB has little effect on track-bridge interaction. The distributions of the four indexes make it possible to design CWR on bridges with the limit state method.
文摘Manuscript received 30 July 1999 Abstract The shielded metal arc welding (SMAW) of a manganese steel part as a crossing of railway track to a carbon steel part as the rails of the railroad is the welding of dissimilar steel. It are was known that it is not possible to the the rail of railroad directly to the cross- ing of railway track made from a steel containing about 14% of manganese (wt. ) because of so many differences between the two kinds of steels such as composition, microstructure,mechanical properties and weldability.A method was used to solve the problem by presetting an intermediate layer on each side of the joint and other special procedures were used.The result of test indicated that a good weld joint was obtained.
基金supported by the Major Research Project of Ministry of Railway of China (Grant No. 2010G006-H)
文摘It is known from our former theoretical analysis that the single-inclined welding surface which is inclined towards the transverse direction of the rail can only eliminate vertical bumping, and the single-inclined welding surface which is inclined towards the vertical direction of the rail can only eliminate lateral vibration. In this paper, we put forward a welding structure of double-inclined welding surface to eliminate the vertical bumping and lateral vibration at the same time, and analyze the stress state of continuous welded rail (CWR) by combining geometrical azimuth. Furthermore, the increase of bearing capacity of CWR with the double-inclined welding surface is theoretically analyzed.